In the auction's first day, Cook had gotten 52 bids, starting at $5,000 and spiraling upward quickly. The leading bid Thursday evening was $210,000, and there were still 19 days to go until bidding closes May 14.

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The coffee chat will happen at Apple's Cupertino, California, headquarters. The winner may bring along one guest.

The move fits in with the more open public persona Cook has adopted since replacing late Apple CEO and co-founder Steve Jobs. One of the knocks on Jobs was that he never contributed much of his considerable fortune, or celebrity, to charity -- at least not in the public ways other tech titans like Microsoft's Bill Gates and Facebook's Mark Zuckerberg have.

By some measures, a $180,000 coffee meeting with the chief of the world's leading tech company might be a bargain. An anonymous bidder paid $3.4 million last year for lunch with investor Warren Buffett.

Other celebs taking part in the auction for the RFK Center include Robert DeNiro, Alex Trebek, Carrie Underwood, Peyton Manning, William Shatner and David Letterman.

But if you think Apple's typical hyper-controlling approach to its world will be relaxed during Cook's coffee klatch, think again. For one, there will be no live-tweeting.

"The winner cannot blog, social network, talk to press, write about, take pictures or record during the experience in any way due to security regulations," reads the auction's legal terms.

Visitors will be required to sign a nondisclosure agreement and are subject to a security screening.

"We expect all winning bidders and their guests to conduct themselves appropriately when attending an experience won at Charitybuzz," the terms continue. "Polite manners and respect for the generous donor and adherence to any rules or parameters are a must."

Travel and lodging for the visit, which will last between 30 minutes and an hour, are not covered. No word on whether Cook will pick up the tab for the coffee.